assumption is violated. This is especially attractive when modeling multiple ordinal
variables. We avoid the need to check that each variable meets the parallel regressions
assumption. A similar model with a mixture of normals distribution for the latent
probit score is introduced in Kottas et al. (2005). They use a non parametric mixture.
Our model differs by using a finite mixture, introducing a regression on covariates and
using patient-specific random effects. Besides these innovations, the most important
contribution of this work is the application to inference for adverse event rates.
This chapter builds on earlier work by Zhou (2005), who used a construction with
nested categorical and ordinal models. The rest of the chapter is organized as follows.
In Section 2.2 we briefly describe the clinical trials that a drug has to pass successfully
in order to reach the market. In this section we also present the model by Albert
and Chib (1993) for the Bayesian analysis of binary data and its extension to ordinal
data. In Section 2.3, we introduce a phase III clinical trial. In Section 2.4, we present
a joint multinomial and ordinal probit model to estimate the cell probabilities of
multiple categorical outcomes with different ordinal levels nested in each categorical
outcome. The prior specifications and posterior inference are discussed in Section 2.5.
We illustrate properties of the model by applying the model to a simulated dataset
and data from a phase III clinical trial. The results are presented in Section 2.6. A
summary and discussion of possible extensions are presented in Section 2.7.
2.2 Background
In this section, we present the bio-medical and statistical background of the work
presented in this chapter. First, we explain what a clinical trials is. Later, we briefly
introduce the models proposed by Albert and Chib (1993) for the Bayesian analysis
of binary and ordinal data. Both models exploit the idea of data augmentation by
introducing a latent variable. The same idea is used in the statistical model we
propose in this chapter.